Same thing that creates mirages, the atmosphere bends the light and you can see object that are beyond your horizon. The air is not uniform, there is a big change in temperature and density with altitude, also local atmospheric conditions will have an effect. The result is that the air acts as a giant lens. Also related to the reason why sky is blue and sun is red when it's low.

I was at Burningman too and became kind of obsessed with this question myself.

The above is basically correct. I'd only add one interesting (too me at least ) note. The effect which causes the beam to bend toward the earth is due to the change in air density (lower at higher elevation). The effect from temperature usually is trying to bend the light in the opposite direction away from the earth (like a mirage), but the temperature effect is much less prominent, so air density wins out and we get this cool effect where the beam follows the curve of the earth to some extent: about 3.26 inches per mile ignoring temperature. Which is smaller than the 8 inches per mile of the curve of the earth, but that's a good thing! If the change in density were that great light would reflect back to us and we wouldn't be able to see the sky/stars clearly! Which BTW is a phenomenon which occurs in nature sometimes when there is a temperature inversion (colder lower warmer higher) and when this happens the phenomena is called a superior mirage, because you see the ground reflected off of the "sky" rather than the sky off of the ground.

There is a simple explanation for this effect based on perspective illusion. Here's an example:

Stand in front of a wall in a large room, say the living room of your house. Look up to where the wall meets the ceiling, then to one corner. Now move your eyes smoothly along the line from one corner to the other, noting the apparent change in angle from one corner to the other.

Now, picture yourself standing under a laser beam projected between two one hundred foot high towers each tower being opposite the observer at a distance of several hundred feet. Looking at one tower, the beam appears to be rising toward the zenith. Looking at the opposite tower the beam appears to be falling from the zenith to the tower. The laser beam thus appears to rise from one tower and fall toward the other as you sweep your eyes from one to the other... appearing to curve over your head from one tower to the other.

Now think of the OP's situation of a laser several kms away, shining over your head.

This applies no matter what the (clear) atmospheric conditions may be.

A natural version of this phenomenon: Sometimes just after sunset one can see sun rays shining upward over distant mountains, and converging at an opposite point on the eastern horizon.

i saw this effect last year. what was happening was it was being shot from a tower, close to horizontally. from your viewpoint, since it was coming towards you, it looked like it was going up. now jumping to once it passed you, it was heading towards the mountains in the distance, making it look like it curved down and to the side. when i first saw it, i was bewildered as well, but with a couple substances and some time, i was able to figure it out cool illusion, though. look for some wide shots of the playa from wither this year or last, and you can see that the line is actually straight. since it's just a single line in the sky, it's hard to determine height.